[en] The alignment of a set of objects by means of transformations plays an important role in computer vision. Whilst the case for only two objects can be solved globally, when multiple objects are considered usually iterative methods are used. In practice the iterative methods perform well if the relative transformations between any pair of objects are free of noise. However, if only noisy relative transformations are available (e.g. due to missing data or wrong correspondences) the iterative methods may fail. Based on the observation that the underlying noise-free transformations lie in the null space of a matrix that can directly be obtained from pairwise alignments, this paper presents a novel method for the synchronisation of pairwise transformations such that they are globally consistent. Simulations demonstrate that for a high amount of noise, a large proportion of missing data and even for wrong correspondence assignments the method delivers encouraging results.
Disciplines :
Ingénierie, informatique & technologie: Multidisciplinaire, généralités & autres
Auteur, co-auteur :
BERNARD, Florian ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
THUNBERG, Johan ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Gemmar, Peter
HERTEL, Frank ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
HUSCH, Andreas ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
GONCALVES, Jorge ; University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
A solution for Multi-Alignment by Transformation Synchronisation
Date de publication/diffusion :
2015
Nom de la manifestation :
IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
Lieu de la manifestation :
Boston, Etats-Unis
Date de la manifestation :
8-10 June, 2015
Titre de l'ouvrage principal :
The proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
Maison d'édition :
IEEE
Peer reviewed :
Peer reviewed
Projet FnR :
FNR8864515 - Set Convergence In Nonlinear Multi-agent Systems, 2014 (01/02/2015-31/01/2017) - Johan Thunberg
K. S. Arun, T. S. Huang, and S. D. Blostein. Least-squares fitting of two 3-D point sets. Pattern Analysis and Machine Intelligence, IEEE Transactions on, (5):698-700, 1987
A. Bartoli, D. Pizarro, and M. Loog. Stratified generalized procrustes analysis. International Journal of Computer Vision, 101(2):227-253, 2013
K. N. Chaudhury, Y. Khoo, and A. Singer. Global registration of multiple point clouds using semidefinite programming. arXiv. org, June 2013
H. Chui and A. Rangarajan. A new point matching algorithm for non-rigid registration. Computer Vision and Image Understanding, 89(2):114-141, 2003
T. F. Cootes and C. J. Taylor. Active Shape Models-Smart Snakes. In In British Machine Vision Conference, pages 266-275. Springer-Verlag, 1992
D. W. Eggert, A. Lorusso, and R. B. Fisher. Estimating 3-D rigid body transformations: a comparison of four major algorithms. Machine Vision and Applications, 9(5-6):272-290, Mar. 1997
M. A. Fischler and R. C. Bolles. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6), June 1981
J. C. Gower and G. B. Dijksterhuis. Procrustes problems, volume 3. Oxford University Press Oxford, 2004
R. Hadani and A. Singer. Representation theoretic patterns in three dimensional Cryo-Electron Microscopy I: The intrinsic reconstitution algorithm. Annals of mathematics, 174(2):1219, 2011
R. Hadani and A. Singer. Representation Theoretic Patterns in Three-Dimensional Cryo-Electron Microscopy II-The Class Averaging Problem. Foundations of computational mathematics (New York, N. Y.), 11(5):589-616-616, 2011
T. Heimann and H.-P. Meinzer. Statistical shape models for 3D medical image segmentation: A review. Medical Image Analysis, 13(4):543-563, 2009
B. K. P. Horn. Closed-form solution of absolute orientation using unit quaternions. Journal of the Optical Society of America A, 4(4):629-642, 1987
B. K. P. Horn, H. M. Hilden, and S. Negahdaripour. Closedform solution of absolute orientation using orthonormal matrices. Journal of the Optical Society of America A, 5(7):1127, 1988
D. Pachauri, R. Kondor, and V. Singh. Solving the multiway matching problem by permutation synchronization. In Advances in neural information processing systems, pages 1860-1868, 2013
D. Pizarro and A. Bartoli. Global optimization for optimal generalized procrustes analysis. In Computer Vision and Pattern Recognition (CVPR), 2011 IEEE Conference on, pages 2409-2415. IEEE, 2011
P. H. Schönemann. A generalized solution of the orthogonal procrustes problem. Psychometrika, 31(1):1-10, Mar. 1966
A. Singer and Y. Shkolnisky. Three-Dimensional Structure Determination from Common Lines in Cryo-EM by Eigenvectors and Semidefinite Programming. SIAM journal on imaging sciences, 4(2):543-572, June 2011
O. Van Kaick, H. Zhang, G. Hamarneh, and D. Cohen Or. A survey on shape correspondence. In Computer Graphics Forum, pages 1681-1707. Wiley Online Library, 2011
M. W. Walker, L. Shao, and R. A. Volz. Estimating 3-D location parameters using dual number quaternions. CVGIP: Image Understanding, 54(3):358-367, Nov. 1991.
